In A Wealth of Numbers, we have the end product of what must have been a lot of challenging research. Some of the essays reproduced in this volume are obscure in the extreme; some authors have vanished so completely that nothing else is known about them. If one Wardhaugh Thompson had not had the editor’s last name as his first name, his contribution to accounting and proportional reasoning might have been lost forever, which would have been a loss for mathematics. The result of all that apparent effort is a fine collection of essays and stories about mathematics and associated subjects such as astronomy and navigation.

Mathematical notation is preserved as much as possible in these excerpts, which brings to light the changes that have occurred there. That’s something a reader might expect. One perhaps unintentional discovery to be made in this book is the change in the English language in the past 500 years. A 1481 translation of a 1246 essay on the quadrivium of the liberal arts is lightly paraphrased, but the sentence structure and verb forms continue to project what is almost a different language. Grappling with the English and the notation brings a pleasant new level of challenge to what will be familiar material to many readers.

This book works well for random browsing as well as for sustained reading; purely recreational essays and puzzle problems are well-mixed with more serious topics such as an article explaining Cantor’s diagonalization proof and “Cubic equations for the practical man”. There’s something in here for everyone, and it’s a great contribution to the mathematics literature to have it all in one place.

Mark Bollman (mbollman@albion.edu) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.